Problem: Simplify the following expression: $q = \dfrac{-3a^2 + 18a + 48}{a - 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ q =\dfrac{-3(a^2 - 6a - 16)}{a - 8} $ Then we factor the remaining polynomial: $a^2 {-6}a {-16} $ ${-8} + {2} = {-6}$ ${-8} \times {2} = {-16}$ $ (a {-8}) (a + {2}) $ This gives us a factored expression: $\dfrac{-3(a {-8}) (a + {2})}{a - 8}$ We can divide the numerator and denominator by $(a + 8)$ on condition that $a \neq 8$ Therefore $q = -3(a + 2); a \neq 8$